On rising magnetic flux tube and formation of sunspots in a deep domain

We investigate the rising flux tube and the formation of sunspots in an unprecedentedly deep computational domain that covers the whole convection zone with a radiative magnetohydrodynamics simulation. Previous calculations had shallow computational boxes (<30 Mm) and convection zones at a depth of 200 Mm. By using our new numerical code Radition and RSST for Deep Dynamics (R2D2), we succeed in covering the whole convection zone and reproduce the formation of the sunspot from a simple horizontal flux tube because of the turbulent thermal convection. The main findings are as follows. (1) The rising speed of the flux tube is larger than the upward convection velocity because of the low density caused by the magnetic pressure and the suppression of the mixing. (2) The rising speed of the flux tube exceeds 250 m s(-1) at a depth of 18 Mm, while we do not see any clear evidence of the divergent flow 3 h before the emergence at the solar surface. (3) Initially, the root of the flux tube is filled with the downflows, and then the upflow fills the centre of the flux tube during the formation of the sunspot. (4) The essential mechanisms for the formation of the sunspot are the coherent inflow and the turbulent transport. (5) The low-temperature region is extended to a depth of at least 40 Mm in the matured sunspot, with the high-temperature region in the centre of the flux tube. Some of the findings indicate the importance of the deep computational domain for the flux emergence simulations.